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%I #12 Jul 27 2022 06:04:34
%S 1,240,111384,61056996,36134640360,22349791271808,14226080375707200,
%T 9239577908667986880,6091267058935364926620,4062233028933305475849600,
%U 2733980882372812975378956480,1853783080629966591378982417800,1264747920529034302126861656883140,867379957865303554725274256161714560
%N G.f.: 3F2([4/9, 5/9, 8/9], [2/3, 1], 729 x).
%C "Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link).
%H Gheorghe Coserea, <a href="/A275459/b275459.txt">Table of n, a(n) for n = 0..300</a>
%H A. Bostan, S. Boukraa, G. Christol, S. Hassani, J-M. Maillard <a href="http://arxiv.org/abs/1211.6031">Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity</a>, arXiv:1211.6031 [math-ph], 2012.
%F G.f.: hypergeom([4/9, 5/9, 8/9], [2/3, 1], 729*x).
%F D-finite with recurrence n^2*(3*n-1)*a(n) -3*(9*n-5)*(9*n-4)*(9*n-1)*a(n-1)=0. - _R. J. Mathar_, Jul 27 2022
%e 1 + 240*x + 111384*x^2 + 61056996*x^3 + ...
%t HypergeometricPFQ[{4/9, 5/9, 8/9}, {2/3, 1}, 729 x] + O[x]^14 // CoefficientList[#, x]& (* _Jean-François Alcover_, Oct 23 2018 *)
%o (PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");
%o read("hypergeom.gpi");
%o N = 12; x = 'x + O('x^N);
%o Vec(hypergeom([4/9, 5/9, 8/9], [2/3, 1], 729*x, N))
%Y Cf. A268545-A268555, A275051-A275054.
%K nonn
%O 0,2
%A _Gheorghe Coserea_, Jul 31 2016
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